Technion Mathematics Colloquium
 
Title: Topology of linkages, statistical physics, and Morse theory
Speaker: Michael Farber (University of Durham)
 
Abstract
A topological approach to the theory of equilibrium phase transitions in
statistical physics is based on the Topological Hypothesis (TH), which
claims that phase transitions are due to changes of the topology of
suitable submanifolds in the configuration space. This approach was
widely discussed and tested in literature, in various models, with
positive and negative conclusions. In my talk I will consider the
anti-ferromagnetic mean-field XY model and study topology of the
sub-energy manifolds. The latter can be interpreted mechanically as
configuration space of a linkage with one telescopic leg. We use methods
of Morse theory to describe explicitly the Betti numbers of this
configuration space. We show that in the presence of an external magnetic
field the model undergoes a single ?total Betti number phase transition?.
The talk is based on joint work with Viktor Fromm.
 
Monday, December 20, at 3:30 p.m. in Amado 232
 
Light refreshments will be served at 3:00 p.m. in the faculty lounge 
on the 8th floor
 
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Technion Math. Net (TECHMATH)
Editor: Michael Cwikel   <techm@math.technion.ac.il> 
Announcement from: Tamar Ziegler   <tamarzr@techunix.technion.ac.il>